# If f(x)= 2x sin(x) cos(x), how do you find f'(x)?

May 15, 2015

Use trigonometry (sine of 2x) to rewrite the function first:

$f \left(x\right) = 2 x \sin x \cos x = x \left(2 \sin x \cos x\right) = x \sin \left(2 x\right)$

Now use the product rule and use the chain rule to get:

$f ' \left(x\right) = \left(1\right) \left(\sin \left(2 x\right)\right) + \left(x\right) \left(\cos \left(2 x\right) \cdot 2\right)$

Simpply to get:

$f ' \left(x\right) = \sin \left(2 x\right) + 2 x \cos \left(2 x\right)$

I know it doesn't look the same as the other answer. Use trigonometric identities to see that the answers are equivalent.